A universal approach to the calculation of the transit light curves

TL;DR

This paper introduces a universal, accurate method for calculating transit light curves of eclipsing binary systems, applicable across various limb-darkening laws and system parameters, with analytical and numerical solutions.

Contribution

It provides a unified approach with analytical expressions for linear and quadratic limb-darkening laws and efficient numerical methods for logarithmic and square root laws.

Findings

Analytical expressions derived for linear and quadratic limb-darkening laws.

Efficient numerical integration methods developed for complex limb-darkening laws.

Applicable to a wide range of system parameters and limb-darkening models.

Abstract

We have developed a universal approach to compute accurately the brightness of eclipsing binary systems during the transit of a planet in front of the stellar disk. This approach is uniform for all values of the system parameters and applicable to most limb-darkening laws used in astrophysics. In the cases of linear and quadratic limb-darkening laws we obtained analytical expressions for the light curve and its derivatives in terms of elementary functions, elliptic integrals and piecewise-defined function of one variable. In the cases of logarithmic and square root laws of limb darkening the flux and its derivatives were expressed in terms of integrals which can be efficiently computed using Gaussian quadrature formula, taking into account singularities of the integrand.